S000755


For the primes p in S000754, the sum_{1..(p-1)/4} Legendre(i/p), which is a new maximum.

1, 2, 3, 4, 6, 7, 8, 11, 15, 16, 17, 20, 23, 25, 30, 36, 39, 42, 50, 54, 56, 58, 63, 66, 71, 73, 77, 80, 81, 84, 95, 99, 105, 117, 119, 120, 123, 136, 146, 149, 150, 166, 174, 176, 190, 194, 207, 208, 212, 233, 234, 247, 260, 261, 265, 267, 278, 280, 281, 284

1

S000755

Here Legendre(i/p) is the Legendre symbol.

T. D. Noe, Plot of 100 terms

T. D. Noe, Table of 100 terms

Eric W. Weisstein, MathWorld: Legendre Symbol

(Mma) t = {}; mx = 0; n = 0; While[Length[t] < 50, n++; p = Prime[n]; If[MemberQ[{1, 5}, Mod[p, 8]], s = Plus @@ JacobiSymbol[Range[(p - 1)/4], p]; If[s > mx, mx = s; AppendTo[t, {p, s}]]]]; Transpose[t][[2]]

Cf. S000752-S000754.

nonn,hard

T. D. Noe, Nov 20 2015

© Tony D Noe 2014-2015